A communication system requires noncoherent detection when it is infeasible for the receiver to maintain a reliable estimate for instantaneous channel gain (magnitude and, especially, phase). Noncoherent communication systems include, for instance, a wireless multiple access system where the mobile, having limited power, cannot afford to transmit high power known symbols (pilots) to enable reliable channel estimation. A noncoherent communication channel may possess some coherence property: A coherent block is a time interval during which the channel variations are negligibly small. Communication over such a channel is referred to as block-coherent communication.
Block-coherent communication may arise naturally in fast frequency-hopping orthogonal frequency division multiple (OFDM) access systems. In such systems information may be modulated onto a subset of available frequencies, called tones, in every symbol time. To enhance spectral efficiency and increase diversity gain, tones utilized are, in some cases, rapidly hopped across the entire utilized frequency band in every L symbols, i.e., L consecutive symbols are mapped to one tone, followed by another L symbols mapped to a different tone, and so on. When L is small, we can assume consecutive L symbols experience identical channel gain. Although the amplitudes of the gains of two consecutive L symbols can be close, their phases are normally completely independent.
More precisely, a block-coherent communication system can be defined as follows: for a system represented in discrete time domain, the channel gain is an unknown complex random variable that remains the same for every L consecutive symbols but otherwise varies independently according to some distribution, e.g., the phase is uniformly distributed over [0, 2PI] and the magnitude is Rayleigh distributed.
For block-coherent communication the nominal modulation scheme is differential M-array phase-shift-keying (DMPSK). DMPSK carries the information in the phase differences between two successive symbols over the coherent block. For illustration, to transmit N×(L−1) MPSK information symbols s(i), each of the N consecutive sets of L−1 symbols, denoted as s(1), s(2), . . . , s(L−1), is differentially encoded to transmitted symbols t(1), t(2), . . . , t(N), where t(1)=1, and t(j+1)=t(j)×s(j) for j=1, . . . , N−1.
Modulations other than DMPSK are possible. For instance, with the insertion of known symbols in a block, information symbols may be transmitted directly on other symbols instead of differentially. This may be referred to as pseudo-pilot modulation. It is apparent, however, that at most L−1 information symbols can be transmitted inside a dwell of length L due to the phase uncertainty. In general we assume there are M information symbols transmitted in each dwell, which can be regarded as a transmission unit. In other words, each transmission unit includes L–M known symbols. M is at most L−1. For instance, both schemes mentioned have M=L−1.
With forward error-correction coding a block-coherent communication system will normally include an encoder (which inserts structured redundancy into original data stream), a DMPSK modulator (which maps binary data bits to MPSK symbols), a demodulator (which extracts out soft information differentially and feeds it to the decoder), and a decoder (which decodes the original message based on soft information from the demodulator).
In most coded systems, a receiver applying iterative demodulation and decoding—a scheme henceforth referred to as turbo equalization—has significant performance gain over a non-iterative receiver. For instance, convolution and/or turbo coded DMPSK systems, investigated by Shamai et al. in “Iterative decoding for coded noncoherent MPSK communications over phase-noisy AWGN channel” published in IEE Proceedings Communication 2000, demonstrates turbo-equalization performance within 1.3 dB of channel capacity and 1 dB better than traditional schemes.
It has been shown that for turbo equalization to be maximally effective, the code design needs to take the effect of iterative demodulation into account. The necessity of code design and an effective way of achieving it are described in Jin and Richardson's paper “Design of Low-Density Parity-Check Codes in Noncoherent Communication,” published in International symposium on information theory Jun. 30, 2002. The approach therein improves the performance to within 0.7 dB of channel capacity.
For optimal performance of turbo equalization, the coded bits also should be sufficiently interleaved in transmission. The interleaving serves two purposes. On one hand, it can effectively eliminate the correlation among soft-messages associated with coded bits of small distance in the block structure for decoding purposes. On the other hand, interleaving can eliminate the dependence among the soft values feed back to the same coherent block for demodulation. A commonly conceived interleaving structure is random interleaving. To achieve random interleaving, however, the same (randomly generated) permutation must be accessible, e.g., stored, at both the transmitter and the receiver. This inflicts large memory requirements for practical systems coded by large block codes.
While the performance of turbo equalization is important, for a communication system to be practical for use in a wide range of devices, e.g., consumer devices, it is important that the turbo equalizations be capable of being implemented at reasonable cost. Accordingly, the ability to efficiently implement turbo equalization schemes used for a block-coherent communication system, e.g., in terms of hardware costs, can be important.
The usage of LDPC codes as a coding scheme in block-coherent communication is desirable given its near-capacity coding gain and rich design space.
LDPC codes are often represented by bipartite graphs, called Tanner graphs, in which one set of nodes, the variable nodes, correspond to bits of the codeword and the other set of nodes, the constraint nodes, sometimes called check nodes, correspond to the set of parity-check constraints which define the code. Edges in the graph connect variable nodes to constraint nodes. A variable node and a constraint node are said to be neighbors if they are connected by an edge in the graph. For simplicity, we generally assume that a pair of nodes is connected by at most one edge.
A bit sequence associated one-to-one with the variable nodes is a codeword of the code if and only if, for each constraint node, the bits neighboring the constraint (via their association with variable nodes) sum to zero modulo two, i.e., they comprise an even number of ones.
The number of edges attached to a node, i.e., a variable node or a constraint node, is referred to as the degree of the node. A regular graph or code is one for which all variable nodes have the same degree, j say, and all constraint nodes have the same degree, k say. In this case we say that the code is a (j,k) regular code. These codes were originally invented by Gallager (1961). In contrast to a “regular” code, an irregular code has constraint nodes and/or variable nodes of differing degrees. For example, some variable nodes may be of degree 4, others of degree 3 and still others of degree 2.
While irregular codes can be more complicated to represent and/or implement, it has been shown that irregular LDPC codes can provide superior error correction/detection performance when compared to regular LDPC codes.
An exemplary bipartite graph 200 determining a (3,6) regular LDPC code of length ten and rate one-half is shown in FIG. 2. Length ten indicates that there are ten variable nodes V1–V10, each identified with one bit of the codeword X1–X10, the set of variable nodes V1–V10 is generally identified in FIG. 2 by reference numeral 202. Rate one half indicates that there are half as many check nodes as variable nodes, i.e., there are five check nodes C1–C5 identified by reference numeral 206. Rate one half further indicates that the five constraints are linearly independent, as discussed below.
While FIG. 2 illustrates the graph associated with a code of length 10, it can be appreciated that representing the graph for a codeword of length 1000 would be 100 times more complicated.
The practical challenges posed by turbo equalization, in the light of implementation cost, are the complexity of soft-in soft-out (SISO) demodulator and the data interleaving at the transmitter and the receiver. There remains a need for improved interleaving techniques and/or implementation. The present invention is directed to implementing an interleave in an efficient manner. The data interleaving techniques of the present invention are well suited for use with data bits encoded, e.g., by Low Density Parity Check (LDPC) codes.